Avonte Oquendo was last seen at about 12:40 p.m. on Oct. 4 walking out of the Riverview School in Long Island City.

The NYPD said it has 50 officers a day searching for the boy, who doesn’t speak and has trouble performing many basic tasks.

A city schools spokeswoman declined to comment on the potential lawsuit. City schools Chancellor Dennis Walcott has said the city is focused first on finding the student and declined to comment on whether school officials acted properly.

“City schools are safe and we are taking a look at procedures at this particular school and what needs to be tightened up,” Mr. Walcott said Friday. “We are doing an investigation about what happened, but right now our focus is finding the child.”

Avonte’s mother, Vanessa Fontaine, described him as a sweet, loving child who liked to play with his tablet and watch cooking shows. Avonte, who was diagnosed at age 2 1/2, can’t perform some simple tasks such as tying his shoes by himself, and often needs verbal prompts to do things like put on his shirt. He had just arrived at the school as a freshman this year, she said.

“I knew that Avonte would always need someone to watch him,” she said. “I would tell all his teachers, ‘Please keep a close eye on Avonte.’”

The notice of claim filed Wednesday with the city comptroller’s office said the school failed to properly supervise Avonte, who “has a propensity to run away,” causing emotional and psychological harm to the mother and child.

Ms. Fontaine said that over the summer, Avonte had unlocked the doors at the family’s Rego Park home, walked away and was quickly found by police on a local subway platform.

Two days ago, police ordered the Metropolitan Transportation Authority to briefly cut power on the 7 and G lines in the area of the school during a search. Since then, police have been searching subway trains in other parts of the city.

For example, on Thursday evening at the 14th street stop of the 1, 2, 3 line, the conductor announced over the loudspeaker that they were looking for the boy. Avonte’s name was displayed on the information board used to display train arrivals, and a pair of police officers searched the train car-by-car. After searching the last car, they waved to the conductor and the train departed.

Peter J. Smith for The Wall Street Journal

Residents have set up a relief and information station for volunteers searching for a missing autistic boy in Long Island City.

Ms. Fontaine, a single mother with four other sons, said the school called her an hour after Avonte disappeared. She arrived about an hour after that, she said. School officials asked her to make an announcement over the school’s loudspeaker, in case he was hiding somewhere in the school. The family’s attorney, David Perecman, said the family was told there was a fight in the lunchroom that distracted some aides.

The school is used by students with and without special needs. Ms. Fontaine said Avonte is in District 75, the Department of Education’s program for children with the most severe needs.

Mr. Walcott said Thursday that Avonte’s individualized education plan required him to have not more than six students in a class with one teacher and one paraprofessional.

The family plans to hold a vigil at 5 p.m. Friday across the street from the school. Ms. Fontaine’s lawyer’s office said the family has received two offers of rewards, one for $5,000 and another for $50,000 for information that leads to the boy’s safe return.